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In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, wha

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Question: In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)

Options:

  1. 5 cm
  2. 10 cm
  3. 8 cm
  4. 7 cm

Correct Answer: 5 cm

Exam Year: 2020

Solution: 

Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.

In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, wha

Practice Questions

Q1
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
  1. 5 cm
  2. 10 cm
  3. 8 cm
  4. 7 cm

Questions & Step-by-Step Solutions

In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
  • Step 1: Identify the right triangle and the given information: one angle is 30 degrees and the hypotenuse is 10 cm.
  • Step 2: Recall the relationship between the angles and sides in a right triangle. The side opposite the 30-degree angle can be found using the sine function.
  • Step 3: Use the sine function: sin(30°) = opposite side / hypotenuse.
  • Step 4: Substitute the known values into the equation: sin(30°) = opposite side / 10 cm.
  • Step 5: Since sin(30°) equals 1/2, rewrite the equation: 1/2 = opposite side / 10 cm.
  • Step 6: To find the opposite side, multiply both sides by 10 cm: opposite side = 10 cm * 1/2.
  • Step 7: Calculate the result: opposite side = 5 cm.
  • Trigonometric Ratios in Right Triangles – Understanding how to use sine, cosine, and tangent to find the lengths of sides in right triangles based on given angles.
  • Properties of Special Right Triangles – Recognizing the properties of 30-60-90 triangles, where the sides have specific ratios.
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